They take Chemistry, do they also take Physics?

Question

In a class of 150 students, 90 take Physics and 60 do not. Among the 90 Physics students, 50 also take Chemistry. Among the 60 non-Physics students, 20 take Chemistry. You pick a student at random and they take Chemistry. What is the probability they also take Physics?

Accepted Answer

The clue "takes Chemistry" restricts you to Chemistry students, so count them first. - Physics students taking Chemistry: 50. - Non-Physics students taking Chemistry: 20. Total Chemistry students: 50 + 20 = 70. Of those, the ones who also take Physics number 50: P(	ext{Physics} \mid 	ext{Chemistry}) = \frac{50}{70} = \frac{5}{7} \approx 0.714. The denominator is the Chemistry group (70), not the whole class of 150. Takeaway. Conditioning zooms into the subgroup named by the clue; the answer is that subgroup split by the target attribute.

They take Chemistry, do they also take Physics?

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